Cleaning of hollow fibre filters

ABSTRACT

In the cleaning and removal of solids from microporous hollow fibre filters by a series of chemical cleaning cycles, the optimum time and pattern of the cleaning cycles is calculated from the rate of diminution in filtrate flow rate and the time and filtrate lost in each cycle.

FIELD OF INVENTION

This invention relates to the cleaning and removal of solids frommicroporous hollow fibre filters.

BACKGROUND ART

International Patent Applications PCT/AU84/00192 and PCT/AU86/00049describe methods for backwashing elastic microporous hollow fibrefilters. In these filters, a bundle of fibres is contained in a shell orhousing and the liquid to be filtered, known as the feedstock, isapplied to the outside of the fibres.

During the filtering operation, which may be either to recover clarifiedliquid or to recover concentrated solids, some of the liquid containedin the feedstock passes through the walls of the fibres and is drawn offfrom the fibre lumens as filtrate.

Solids contained in the feedstock either pass out of the shell with theremainder of the feedstock carrier stream, or are retained on or in thefibres. These retained solids cause fouling and blockage of the filter.

Industrial practice with the common tube-in-shell microfilters for manyyears was to apply the feedstock to the inner surface of the fibres byforcing flow through the fibre lumens at such a rate that turbulencescoured the walls of the fibres, retarding blockage by solid material.

In the filter systems described in the above mentioned InternationalPatent Applications, the feedstock is applied to the outer surface ofthe fibres, with a penalty of low feedstock flow velocity and lowturbulence resulting in a rapid rate of blockage of the pores of thefibres.

The blockage of pores is overcome by the application of a backwashingcycle. In the first stage of the cycle, a liquid backwash is applied tothe lumens of the fibres such that the liquid passes through the porouswalls of the fibres and sweeps retained solids out of substantially allof the pores in the walls of the fibres. In the second stage, a gaseousbackwash is applied to the lumens of the fibres such that the gas passesthrough the larger pores in the walls of the fibres, stretching them anddislodging retained blocking solids.

The application of the backwashing cycle discussed above restoresfiltrate flux to a high value that is, however, not as high as theinitial value. Part of the drop in flux is due to the retention of somesolids in the pores of the fibres. With each cycle this slightdiminution of the flux reduces the filtration capacity of the fibres.Eventually chemical cleaning is required which is expensive and timeconsuming.

The need to optimise the frequency of cleaning cycles so as to maximisefiltrate flow is discussed in our International Patent ApplicationPCT/AU84/00192, where it is pointed out that it is necessary to maximisethe total amount of permeate flow, and minimise the time and permeatelost in a backwash cycle.

In most cases, the filtration process is characterised by a depositionof a layer of solid material on the filter surface that then acts as afilter surface itself. This layer may be constantly changing and isknown in the art as a dynamic membrane. In tube-in-shell filters, theconstant change in the layer is, in part, caused by the method ofapplication of the feed, which is to apply it in a direction of flowparallel to the fibres, known as cross-flow filtration. The layer isthus potentially being deposited and swept off at the same time.

The dynamic membrane may be unwanted, or it may be beneficial. There arecases where a filter's rejection of solid material is poor until asufficient layer of dynamic membrane has built up on the filter to givean acceptable product. The dynamic membrane may be composed of solidsfrom the feed, or it may be primarily composed from added filter aidmaterials.

When a dynamic membrane is desired, care must be taken to ensure thatthe backwash cleaning cycle is vigorous enough to dislodge blockingsolids, but not so vigorous as to sweep away too much of the dynamicmembrane. When too much of the dynamic membrane is swept away by thebackwash, the filtrate must be diverted back to the feed tank untilsufficient dynamic layer is built up again.

In many selective separation cases it has been found that a series ofliquid-only backwashes is adequate, with an occassional gaseousbackwash. The aim in these cases then, is to maximise the volume offiltrate in a given time, while at the same time ensuring that thequality of the filtrate is maintained.

DISCLOSURE OF THE INVENTION

According to one aspect of the invention there is provided a method ofoptimising the cleaning of a hollow fibre filter comprising the stepsof:

(i) calculating from the rate of diminution of the filtrate flow rateafter each application of a pressurised liquid and/or gaseous backwashcleaning cycle an equation expressing the relationship between filtrateflow and time, and,

(ii) allowing for the time lost in each backwash cycle and the amount offiltrate lost in each backwash cycle, and,

(iii) calculating from filtrate loss, the time loss and the relationshipbetween filtrate flow rate and time, the optimum time of application ofliquid and/or gaseous backwashes.

The invention may be modified by optimising the time for chemicalcleaning either with or without the backwash optimisation by calculatingfrom the rate of decrease of peak value of filtrate flow after eachbackwash cycle and the time and amount of filtrate lost in a shut downfor chemical cleaning, the optimum time for shut down for chemicalcleaning.

According to another aspect of the invention there is provided a methodof operating a microporous hollow fibre filter which employs theoptimisation techniques described above.

The invention also provides apparatus for filtering a feedstock and forautomatically calculating and applying the optimal backwash cycles asdescribed above, said apparatus comprising:

(i) means for applying a feedstock to be filtered to the outside surfaceof porous hollow fibres contained in a shell or housing; and forwithdrawing clarified liquid or filtrate from the lumens of the fibres,

(ii) means for applying through the fibre lumens liquid and gaseousbackwashes that pass through the walls of the fibres,

(iii) means for measuring the rate of decrease in filtrate flow rate, orflux,

(iv) means for calculating the optimal backwash frequency taking accountof the loss of filtrate and time involved in a backwash cycle, and,

(v) means for applying the calculated optimal backwash frequency to thefibres in the filter.

The optimising method of the invention may be employed to maintain adynamic membrane over the surfaces of the fibres. This can be achievedby allowing the filtrate to be returned to the feedstock until thedynamic membrane has built up on the fibres which will be evidenced bythe quality of the filtrate. After each liquid and/or gaseous backwashstep, the filtrate is returned to the feedstock until the dynamic layerhas again been built up on the filters.

According to another aspect of the invention there is provided a methodof cleaning a hollow fibre filter in which the fibres are subjected to aseries of cleaning cycles characterised in that the cleaning cycles areapplied when the integrated filtrate flux over time since the last cycleequals the instantaneous filtrate flux multiplied by the sum of theperiod of time elapsed since the last cleaning cycle plus the time takenfor the cleaning cycle. The invention also embraces apparatus forcarrying out this aspect of the invention. This relationship may beexpressed mathematically as ##EQU1## where t=time

T=a point in time measured from the last cleaning cycle,

T_(c) =time taken to apply a backwash or cleaning cycle,

v(t)=flow rate of filtrate at any point in time t,

v(T)=flow rate of filtrate at the point in time T

The derivation of this relationship is as follows:

The aim is to operate the filter at maximum average production rate,APR. APR is given by the expression ##EQU2##

By choosing the time T at which d(APR)/dT=0 we get ##EQU3##

Note that the condition may be written ##EQU4## and it follows that thecondition may never be satisfied if T_(c) is sufficiently large.

The invention also provides apparatus for application of the abovemethod comprising:

(i) means for applying a feedstock to be filtered to the outside surfaceof porous hollow fibres contained in a shell or housing and forwithdrawing filtrate from the lumens of the fibres,

(ii) means for applying through the fibre lumens liquid and gaseousbackwashes that pass through the walls of the fibres,

(iii) means for measuring the volume of filtrate over a period of time,

(iv) means for determining the instantaneous filtrate flow rate at anypoint in time,

(v) means for determining when the volume of filtrate over a period oftime equals the instantaneous filtrate flow rate multiplied by theperiod of time that has elapsed added to a set period of time.

The means for measuring the volume of filtrate over a period of time mayconveniently be an integrating flowmeter or a programmable controller.

The invention also includes methods and apparatus that use thetechniques already described but also allow for costs such as wear andtear induced by a backwash or cost of air in the backwash. Such methodsand apparatus typically add a set period of time to the optimumcalculated by the described methods, or increase the time by a factor.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the invention may be more readily understood and put intopractical effect, reference will now be made to the accompanyingdrawings in which:

FIG. 1 is a schematic diagram of a hollow fibre filter system accordingto one embodiment of the invention,

FIG. 2 is a graph of filtrate flux as a percent of maximum against timeaccording to the theory of the present invention and showing data forone set of test results of Example 1,

FIG. 3 is a further graph of filtrate flux as a percent of maximumagainst time according to the theory of the present invention andshowing data for another set of test results of Example 1,

FIG. 4 is a graph of permeate flux against time over several backwashcycles for a filter system similar to that shown in FIG. 1 as detailedin Example 2, and,

FIGS. 5 to 12 are graphs similar to FIGS. 2 and 3 for the data of runs 1to 8 of Example 3.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In the filter system shown in FIG. 1, a feed tank 20 is connected to thefeed side of a filter unit 21 by feed line 22. Feed line 22 has astrainer 23, a feed pump 24, a check valve 25, a manual valve 26 and apressure gauge 27.

The filter unit 21 includes a cartridge or shell within which ispositioned a bundle of hollow porous, polymeric fibres. In thisinstance, each fibre is made of polypropylene, has an average pore sizeof 0.2 micron, a wall thickness of 200 micron and a lumen diameter of200 micron. There are 3,000 hollow fibres in the bundle but this numberas well as the indivdiual fibre dimensions may be varied according tooperational requirements. A bank of such cartridges may be used.

A concentrate discharge line 28 extends from the feed side of the hollowfibres within the filter unit 21 to the junction of concentrate returnline 29 and concentrate discharge line 30. The concentrate dischargeline 28 has a pressure gauge 31 and a manual valve 32.

Concentrate return line 29 delivers the concentrate through agas-operated valve 33 to the feed tank 20. Concentrate discharge line 30delivers concentrate through a gas-operated valve 34 to a draindischarge outlet 35.

Permeate from the lower ends of the fibre lumens is drawn off throughpermeate line 36 and permeate from the upper ends of the fibre lumens isdrawn off through permeate line 37. Permeate lines 36 and 37 areconnected by line 38 which has a gas-operated valve 39. Main permeateline 40 which has a pressure gauge 41, a gas-operated valve 42, afiltrate quality detector 43, a flowmeter 44 and a manual valve 45delivers filtrate to filtrate discharge outlet 46.

The permeate line 37 is also connected to the drain discharge outlet 35through a gas-operated valve 47.

The filtrate quality detector 43 may be of any convenient kind such as aturbidimeter. The flowmeter 44 may also be of convenient kind such as anintergrating flowmeter.

Pressurised gas, such as air, is supplied through line 48 to an airfilter 49 and pressure regulator 50 to air supply line 51. The airsupply line 51, which has a pressure gauge 52 is controlled bysolenoid-operated valve 53 to provide pressurised air to thegas-operated valve 33.

Pressurised air is also delivered through line 54 to a pressureregulator 55 and solenoid operated valve 56 through line 57 and checkvalve 58 to permeate connection line 38. There is a pressure gauge 59 inair line 57. An air by-pass line 60 leads from air line 54 to permeateconnection line 38 through a solenoid operated valve 61 and check valve62.

A further air line 63 connects the air supply line 51 to gas-operatedvalve 42 in the main permeate line 40. The valve 42 is controlled bysolenoid-operated valve 64 in air line 63. Air line 65 which isconnected between the air supply line 51 and the gas-operated valve 47is controlled by solenoid-operated valve 66. Air line 67 which isconnected between the air supply line 51 and gas-operated valve 39 iscontrolled by solenoid-operated valve 68. Airline 69 which is connectedbetween the air supply line 51 and gas-operated valve 34 is controlledby solenoid-operated valve 70.

A programmable controller 71 receives inputs from the quality meter 43and the flowmeter 44 through lines 72 and 73 respectively. Line 74connects the controller 71 to the feed pump 24.

Lines 75, 76, 77, 78, 79, 80 and 81 are outputs from the programmablecontroller 71 to solenoid-operated valves 53, 70, 68, 66, 64, 61 and 56respectively. Thus, the gas-operated valves 33, 34, 39, 42 and 47 arecontrolled by the programmable controller 71 as are the gas inletsolenoid-operated valves 56 and 61 and the feed pump 24.

In filtration mode, feed from tank 20 enters filtration unit 21 throughline 22. Valves 33, 39 and 42 are open and valves 34 and 47 are closed.Air supply valves 56 and 61 are also closed and feed pump 24 is on. Feedrecirculation or concentrate (that is feed less filtrate) leaves thefilter unit 21 through lines 28 and 29 and returns to the feed tank 20.Clarified liquid or filtrate leaves the top of the filter unit 21through permeate line 37 and flows through line 38 to join filtrateleaving the bottom of the filter unit 21 through permeate line 36. Thefiltrate leaves the system via discharge outlet 46 after passing throughthe quality meter 43 and flowmeter 44. Manual valves 26, 32 and 45 aremanipulated to give the desired line pressures.

The programmable controller 71 is continuously supplied with informationas to the quality and quantity of the filtrate stream (as a function oftime) by the flowmeter 44 and quality meter 43. Within the programmablecontroller 71 there is an optimisation routine which repeatedlymaximises the filtrate flow rate within quality constraints, takingaccount of the time and filtrate lost in a backwash cycle. In effect,the programmable controller 71 evaluates the optimum time betweengaseous or liquid backwashes, and also between chemical cleans whichfollow a series of backwashes. The programmable controller 71 effectsthe gaseous or liquid backwash by manipulation of valves 33, 39, 42, 47and 34, air supply valves 56 and 61 and the feed pump 24.

When a dynamic layer or membrane is desired, filtrate is diverted andreturned to the feed until filtrate quality is acceptable. Filtration isthen commenced with filtrate collected as described above. After abackwash cycle this procedure is repeated if necessary. The loss of timeand filtrate is again taken into account in optimising the choice oftime for backwash.

In the preferred embodiment of the invention, as filtration isoccurring, the programmable controller repeatedly calculates an equationrepresenting the relationship between filtrate flowrate and time, andfrom this and stored information on the loss of time and filtrate inbackwashing, calculates the optimum time for backwash. This procedure isconstantly repeated with consequent refinement of the estimated time toapply a backwash until the point where backwash is to be applied isreached. After the backwash the procedure is repeated for the new cycle.The procedure is made simpler if an integrating flowmeter is used.

In another preferred embodiment, the programmable controller calculatesintegrated flux since the last backwash and applies a backwash when theintegrated flux equals the instantaneous flux multiplied by the sum ofthe period of time elapsed since the last backwash plus the time takenfor a backwash cycle.

The following examples illustrate the technique of the invention. Inexamples 1 to 4, the equation expressing the relationship between flowof filtrate, time and rate of decrease of peak filtrate flow after eachliquid or gaseous backwash step was chosen to be of the form: ##EQU5##where Y represents filtrate flux or flow rate

T represents time

M is a constant

N is a constant

C is a constant representing the flux after a long period of time

EXAMPLE 1

An 80 liter sample containing approximately 3.8 g/1 of diatomaceousearth suspended in water was filtered by continuous recycle through afilter system similar to that shown in FIG. 1 but without theprogrammable controller. The system contained a single tube-in-shellcartridge containing a bundle of hollow porous fibres equivalent toapproximately one square meter of filtration surface. All feed, filtrateand backwashed solids were returned to the feed tank.

Two ten minute runs were conducted in which filtrate flux rate,concentration of feed, and transmembrane pressure were measured everyminute. After the apparatus had settled down, the following results wererecorded (the transmembrane pressure remained substantially constant):

                  TABLE I                                                         ______________________________________                                        TIME   CONCENTRATION  FLUX        % OF                                        (min)  (gm/liter)     (liters/hr) MAX. FLUX                                   ______________________________________                                        RUN 1                                                                         0      3.71           990         100                                         1      3.54           930         93.9                                        2      3.41           900         90.0                                        3      3.29           880         88.9                                        4      3.26           875         88.4                                        5      3.14           850         85.9                                        6      3.09           835         84.3                                        7      3.11           825         83.3                                        8      3.00           820         82.8                                        9      2.97           800         80.0                                        10     2.94           795         80.3                                        RUN 2                                                                         0      3.59           1050        100                                         1      3.51           1000        95.2                                        2      3.38           975         92.9                                        3      3.36           940         89.5                                        4      3.32           925         88.2                                        5      3.26           900         85.7                                        6      3.21           880         83.8                                        7      3.18           875         83.3                                        8      3.21           865         82.4                                        9      3.17           855         81.4                                        10     3.15           850         80.9                                        ______________________________________                                    

In Run 1, the filtrate flow rate or flow decreased from 990 l/hr to 795l/hr over a ten minute period and in Run 2 the flow rate decreased from1050 l/hr to 850 l/hr over a similar period.

An equation (II) was fitted to the results and graphed as shown in FIGS.2 and 3, which refer to Runs 1 and 2 respectively.

The method of fitting the theoretical curve of equation (II) to theresults of Table 1 and the derivation of the constants C, M and Nemployed a least squares curvefit computer programme.

The constants in the equation II used to generate the theoreticalcurves, and the sum of squares were as follows (the standard deviationsare given in brackets):

    ______________________________________                                                    RUN 1       RUN 2                                                 ______________________________________                                        C             71.959 (1.84) 69.119 (1.34)                                     M             12.886 (1.95) 10.048 (0.90)                                     N             1.0           1.0                                               Sum Squares   4.93          1.52                                              ______________________________________                                    

When a correction was made for the rapidly altering concentration(which, in this case, is a result of the limited experimental design),there was very little difference in the degree of fit of theoreticalcurves to the data of Table I.

The concentration correction was made as follows:

Concentration as a percentage of initial contration was calculated (K/Ko%)

These values were fitted to the equation ##EQU6## and the constants k,jand h evaluated.

For Run 1 they were 61.3, 5.88 and 0.91

For Run 2 they were 84.0, 27.86 and 1.216

The equation for K/Ko (equation III) with the calculated values of k, jand h inserted, was then inserted into the equation ##EQU7## and acurvefit run. The values of M, N and C given by this method were verylittle different from the values if no K/Ko correction was made.

An optimum time for air backwash was then calculated, assuming in thiscase that the time lost in backwash was 30 seconds. The optimum time ineach run was 7 minutes.

The Basic programme for this calculation was as follows:

    ______________________________________                                        PROGRAMME A                                                                   ______________________________________                                        10   LPRINT "OPTIMISATION OF GASEOUS BACK-                                         WASH INTERVAL TIME"                                                      20   INPUT "RUN NUMBER";R                                                     30   INPUT "M(HOUR UNITS),C(% OF INITIAL RATE)";                                   M,C                                                                      40   LPRINT"RUN NUMBER"; R;"M=";M;"C=";C                                      50   LPRINT "TIME (HOURS);OPTIMISED OUTPUT                                         (LITERS/HR)"                                                             60   FOR T=O TO 1/3STEP 1/60                                                  70   A=(100-C)*LOG(1+M*T)/M+C*T                                               80   P=A/(T+1/120)                                                            90   LPRINT T,P                                                               100  NEXT T                                                                   Note that line 70 is equivalent to                                            A=[(100-C)*log(1+M*T)/M]+C*T                                                  ______________________________________                                    

In line 70, A equals Integrated flux at time T since ##EQU8##

In line 80, 1/120 is equivalent to a 30 second backwash expressed inhours, so P equals integrated flux divided by the sum of time elapsedsince the last backwash cycle and cleaning time. Thus, P is an averageproduction rate allowing for volume of filtrate lost during backwash,although this volume is not calculated specifically. Line 90 shows theoptimum time as the point where P is a maximum.

Example 1 may also be worked by using equation (I).

The basic programme for this is a follows:

    ______________________________________                                        PROGRAMME B                                                                   ______________________________________                                        10     LPRINT "OPTIMISATION OF GASEOUS BACK-                                         WASH INTERVAL TIME"                                                    20     INPUT "RUN NUMBER";R                                                   30     INPUT "M (HOUR UNITS), C(% OF INITIAL                                         RATE)";M,C                                                             40     LPRINT "RUN NUMBER";R;"M=";"C=";C                                      50     LPRINT "TIME (HOURS) FOR OPTIMISED                                            OUTPUT"                                                                60     FOR T=1 TO 1/3STEP 1/60                                                70     A=((100-C) *LOG(1+M*T))/M)+C*T                                         80     B=(((100-C)/(1+M*T))+C)*(T+1/120)                                      90     P=A-B                                                                  100    LPRINT T,P                                                             110    NEXT T                                                                 ______________________________________                                    

A is the integrated flux at time T and B is the instantaneous flux attime T multiplied by the sum of the time elapsed since last backwashplus the time to clean. With this approach, P is defined as equallingthe integrated flux at time T (A) minus the instantaneous flux (B) sothe optimum time is when P is a minimum. In Example 1 this time is 7minutes.

EXAMPLE 2

50 g bentonite and 50 g diatomaceous earth were suspended in 20 litersof water and applied to a filter system similar to the one used in theprevious Example. Air backwash was applied every 10 minutes and the fluxplotted in FIG. 4. After each backwash the value to which the fluxreturned is shown in Table II.

                  TABLE II                                                        ______________________________________                                        TIME AT BACKWASH   FLUX                                                       (minutes)          (liter/hr)                                                 ______________________________________                                         0                 560                                                        10                 510                                                        20                 450                                                        30                 460                                                        40                 450                                                        50                 480                                                        60                 450                                                        ______________________________________                                    

As can be seen in Table II, the peak value of filtrate flow after eachbackwash cycle decreased from 560 l/hr to 450 l/hr over the six backwashcycles.

Equation II above was used to generate a curve which connected the peakflow rate points, the constants were:

    ______________________________________                                                 C   70.0                                                                      M   2.0                                                                       N   1.0                                                              ______________________________________                                    

An optimum time for chemical cleaning was then calculated assuming thatthe time lost in chemical cleaning would be 1 hour.

The calculation of the optimum time for chemical cleaning is the same asfor Example 1 and uses the same Basic programme but with line 60modified to calculate the average production rate (P) over the timerange 130 to 160 hours in steps of 1 hours, thus:

60 FOR T=130 TO 160 STEP 1

and with line 80 modified to reflect the one hour cleaning time, thus:

80 P=A/ (T+1)

EXAMPLE 3

199.8 g freshly precipitated ferric hydroxide were suspended in 20 1water and filtered by continuous recycle through a filter system similarto that shown in FIG. 1 without the controller. The temperature wasmaintained at 25±2° C. The inlet pressure was 200 KPa(g), the outletpressure was 100 KPa(g), and the filtrate pressure varied from 0 to 45KPa(g). The filtrate flux for eight runs is shown in Table III:

                  TABLE III                                                       ______________________________________                                        Time     Flux   % of       Time    Flux % of                                  mins     1/hr   max flux   mins    1/hr max flux                              ______________________________________                                        Run 1                      Run 5                                              0        740    100.0      0       760  100.0                                 1        595    80.4       1       645  84.2                                  2        525    70.9       2       575  71.7                                  3        475    64.2       3       515  62.5                                  4        425    57.4       4       475  53.8                                  5        400    54.1       5       445  49.5                                  6        375    50.7       6       420  45.7                                  7        350    47.3       7       400  42.4                                  8        330    44.6       8       385  40.8                                  9        310    41.9       9       375  38.6                                  10       295    39.9       10      360  37.0                                  Backwash                   Backwash                                           Run 2                      Run 6                                              0        760    100.0      0       815  100.0                                 1        615    80.9       1       690  84.7                                  2        530    69.7       2       600  73.6                                  3        475    62.5       3       540  66.3                                  4        420    55.3       4       490  60.1                                  5        385    50.7       5       465  57.1                                  6        370    48.7       6       440  54.0                                  7        350    46.1       7       410  50.3                                  8        330    43.4       8       390  47.9                                  9        315    41.4       9       375  46.0                                  10       300    39.5       10      345  42.3                                  Backwash                   Backwash                                           Run 3                      Run 7                                              0        750    100.0      0       810  100.0                                 1        630    84.0       1       695  85.8                                  2        550    73.3       2       605  74.7                                  3        495    66.0       3       540  66.7                                  4        450    60.0       4       500  61.7                                  5        430    57.3       5       460  56.8                                  6        400    53.3       6       440  54.3                                  7        390    52.0       7       415  51.2                                  8        365    48.7       8       395  48.8                                  9        350    46.7       9       380  46.9                                  10       330    44.0       10      360  44.4                                  Backwash                   Backwash                                           Run 4                      Run 8                                              0        760    100.0      0       830  100.0                                 1        645    84.9       1       700  84.3                                  2        580    76.3       2       600  72.3                                  3        525    69.1       3       540  65.1                                  4        485    63.8       4       495  59.6                                  5        460    60.5       5       460  55.4                                  6        430    56.6       6       435  52.4                                  7        410    53.9       7       410  49.4                                  8        395    52.0       8       390  47.0                                  9        375    49.3       9       375  45.2                                  10       360    47.4       10      360  43.4                                  Backwash                   End                                                ______________________________________                                    

An equation (II) was fitted to the results and graphed as shown in FIGS.5 to 12, where FIG. 5 corresponds to Run 1, FIG. 6 to Run 2, and so onup to FIG. 12 which corresponds to Run 8.

The constants used to generate the curves are as shown in the followingTable where the standard deviations are given in brackets. N was verynear to 1 in each case and so was taken as 1 in later calculations.

    ______________________________________                                                                     Sum of                                           Run No.  M          C        Squares Residual                                 ______________________________________                                        1        17.0 (1.0) 20.0 (1.8)                                                                             8.39                                             2        18.6 (0.6) 20.4 (1.0)                                                                             2.75                                             3        16.4 (0.7) 25.0 (1.3)                                                                             3.95                                             4        14.4 (0.5) 26.2 (1.0)                                                                             1.91                                             5        15.6 (0.4) 27.1 (0.7)                                                                             0.94                                             6        14.5 (0.7) 20.6 (1.7)                                                                             5.03                                             7        14.3 (0.5) 21.6 (1.1)                                                                             2.06                                             8        16.7 (0.6) 23.3 (1.0)                                                                             2.24                                             ______________________________________                                    

Calculation of the optimum time for backwash for each of the runs(assuming the time lost in backwash was 30 seconds and taking account offiltrate lost using programmes A and B gave the following results:

    ______________________________________                                               OPTIMUM TIME                                                           RUN      PROGRAMME B   PROGRAMME A                                            ______________________________________                                        1        2.5           2.5                                                    2        2.5           2.5                                                    3        2.5           3                                                      4        2.5           3                                                      5        2.5           3                                                      6        2.5           2.5                                                    7        2.5           3                                                      8        2.5           2.5                                                    ______________________________________                                    

EXAMPLE 4

A suspension of 50 g diatomite and 50 g bentonite in 20 1 water wasfiltered as in Example 3. The temperature was maintained at 25±2° C. Theinlet pressure was 200 KPa(g), the outlet pressure was 100 KPa(g), andthe filtrate pressure varied between 10 and 50 KPa(g). The filtrate fluxfor twelve runs is shown in Table IV.

                  TABLE IV                                                        ______________________________________                                        Time     Flux   % of       Time    Flux % of                                  mins     1/hr   max flux   mins    1/hr max flux                              ______________________________________                                        Run 1                      Run 2                                              0        850    100.0      0       840  100.0                                 1        710    80.7       1       695  83.1                                  2        630    69.9       2       600  72.3                                  3        550    63.3       3       545  65.1                                  4        510    59.0       4       505  60.8                                  5        480    55.4       5       480  57.8                                  6        460    53.6       6       460  55.4                                  7        445    51.8       7       445  53.6                                  8        435    50.6       8       430  51.8                                  9        425    49.4       9       425  51.2                                  10       420    48.2       10      420  50.6                                  Backwash                                                                      Run 3                      Run 4                                              0        830    100.0      0       830  100.0                                 1        670    80.7       1       690  83.1                                  2        580    69.9       2       600  72.3                                  3        525    63.3       3       540  65.1                                  4        490    59.0       4       505  60.8                                  5        460    55.4       5       480  57.8                                  6        445    53.6       6       460  55.4                                  7        430    51.8       7       445  53.4                                  8        420    50.6       8       430  51.8                                  9        410    49.4       9       425  51.2                                  10       400    48.2       10      420  50.6                                  Backwash                   Backwash                                           Run 5                      Run 6                                              0        850    100.0      0       800  100.0                                 1        695    81.8       1       670  83.8                                  2        610    71.8       2       580  72.5                                  3        550    64.7       3       520  65.0                                  4        510    60.0       4       490  61.3                                  5        485    57.1       5       460  57.5                                  6        465    54.7       6       445  55.6                                  7        450    52.9       7       430  53.8                                  8        440    51.8       8       420  52.5                                  9        430    50.6       9       410  51.3                                  10       425    50.0       10      405  50.6                                  Backwash                   Backwash                                           Run 7                      Run 8                                              0        780    100.0      0       750  100.0                                 1        670    85.9       1       650  86.7                                  2        575    73.7       2       565  75.3                                  3        520    66.7       3       520  69.3                                  4        480    61.5       4       480  64.0                                  5        460    59.0       5       455  60.7                                  6        445    57.1       6       440  58.7                                  7        430    55.1       7       430  57.3                                  8        425    54.5       8       420  56.0                                  9        415    53.2       9       410  54.7                                  10       410    52.6       10      405  54.0                                  Backwash                   Backwash                                           Run 9                      Run 10                                             0        850    100.0      0       820  100.0                                 1        680    80.0       1       670  81.7                                  2        585    68.8       2       575  70.1                                  3        530    62.4       3       520  63.4                                  4        490    57.6       4       480  58.5                                  5        470    55.3       5       460  56.1                                  6        450    52.9       6       440  53.7                                  7        430    50.6       7       430  52.4                                  8        420    49.4       8       415  50.6                                  9        410    48.2       9       405  49.4                                  10       400    47.1       10      400  48.8                                  Backwash                   Backwash                                           Run 11                     Run 12                                             0        800    100.0      0       800  100.0                                 1        650    81.3       1       650  81.3                                  2        565    70.6       2       560  70.0                                  3        500    62.5       3       500  62.5                                  4        470    58.8       4       480  60.0                                  5        450    56.3       5       445  55.6                                  6        435    54.4       6       430  53.8                                  7        420    52.5       7       420  52.5                                  8        410    51.3       8       410  51.3                                  9        400    50.0       9       400  50.0                                  10       395    49.4       10      395  49.4                                  Backwash                   End                                                ______________________________________                                    

The constants generated as in earlier Examples are as shown in thefollowing Table where the standard deviations are given in brackets:

    ______________________________________                                        Run                                  Sum of Squares                           No.   M               C      N       Residual                                 ______________________________________                                        1     65.1   (20.2)   41.5 (1.7)                                                                           1.27 (0.08)                                                                           3.560                                    2     52.9   (5.7)    41.8 (0.6)                                                                           1.18 (0.03)                                                                           0.387                                    3     39.9   (3.7)    39.3 (0.6)                                                                           1.09 (0.02)                                                                           0.273                                    4     53.4   (5.9)    42.5 (0.6)                                                                           1.19 (0.03)                                                                           0.408                                    5     43.6   (5.9)    41.1 (0.8)                                                                           1.12 (0.03)                                                                           0.589                                    6     66.9   (7.8)    43.7 (0.6)                                                                           1.25 (0.03)                                                                           0.460                                    7     137.3  (16.8)   48.1 (0.4)                                                                           1.44 (0.03)                                                                           0.482                                    8     82.7   (12.6)   47.9 (0.7)                                                                           1.34 (0.04)                                                                           0.716                                    9     35.1   (4.5)    37.4 (0.9)                                                                           1.05 (0.03)                                                                           0.541                                    10    58.3   (7.1)    41.5 (0.6)                                                                           1.18 (0.03)                                                                           0.493                                    11    65.6   (13.3)   48.9 (1.0)                                                                           1.20 0.05)                                                                            1.323                                    12    62.3   (15.2)   42.6 (1.2)                                                                           1.19 (0.06)                                                                           1.908                                    ______________________________________                                    

The optimum time for backwash (assuming the time lost in a backwash was30 seconds and taking accounts of the amount of filtrate lost) wascalculated using the following programme:

    ______________________________________                                        PROGRAMME C                                                                   ______________________________________                                        10   LPRINT "OPTIMISATION OF GASEOUS BACK-                                         WASH INTERVAL TIME"                                                      20   INPUT "RUN NUMBER";R                                                     30   INPUT "M(HOUR UNITS), C(% OF INITIAL RATE),                                   N";M,C,N                                                                 40   LPRINT "RUN NUMBER";R;"M=;M;"C=";C'"N=";N                                50   LPRINT "TIME (HOURS) FOR OPTIMISED                                            OUTPUT"                                                                  60   Y=O                                                                      70   FOR T=O TO 1/3 STEP 1/720                                                80   A=((100-C)/(1+(M*(T N))))+C                                              90   B=((100-C)/(1+M*((T+1/720) N)))+C                                        100  Y=Y+((A+B)/1440)                                                         110  P=Y/(T+1/120)                                                            120  IF (720*T) MOD (120*T) = 0 THEN 130 ELSE 140                             130  LPRINT T,P                                                               140  NEXT T                                                                   ______________________________________                                    

The optimum time for backwash for each run is shown in Table V.

                  TABLE V                                                         ______________________________________                                               OPTIMUM TIME            OPTIMUM TIME                                   RUN    (minutes)     RUN       (minutes)                                      ______________________________________                                        1      2             7         2                                              2      2             8         2.25                                           3      2             9         2                                              4      2             10        2                                              5      2             11        2.5                                            6      2             12        2                                              ______________________________________                                    

EXAMPLE 5

1300 g TiO₂ suspended in 30 1 water at 50° C. were filtered using anapparatus similar to that in FIG. 1 where the programmable controllercalculated when integrated flux equalled instantaneous flux multipliedby the sum of the period of time elapsed since the last backwash plusthe time taken for a cleaning backwash cycle. In this case the backwashcycle took one minute. The feed inlet pressure was 200 kPa, the feedoutlet 90 kPa, and the filtrate backpressure was zero.

The filtration was then performed using the optimum time and then timesgreater than and less than the optimum time as follows:

(i) the controller selected an optimum time between backwashes ofapproximately 80 seconds. The average production rate was 423 1/hr.

(ii) the filtration was performed with a 6 minute (manually set)interval between backwashes. The average production rate was 271 1/hr.

(iii) the filtration was performed with a 25 second (manually set)interval between backwashes. The average production rate was 279 1/hr.

It can be seen from this Example that where flux falls off rapidly, thecorrect timing between backwashes can make a large difference to theefficiency of the filtration.

EXAMPLE 6

300 g Ca(OH)₂ in 30 1 water at 50° C. were filtered in an experimentsimilar to Example 5. The feed inlet pressure was 150 kPa, the feedoutlet 90 kPa, and the filtrate backpressure zero. Time lost forbackwash was 1 minute.

The filtration was performed using the optimum time and then using timesgreater and less than the optimum time as follows:

(i) the controller selected an optimum time between backwashes ofapproximately 5 minutes The average production rate was 1097 1/hr.

(ii) the filtration was performed with a 10 minute (manually set)interval between backwashes. The average production rate was 1056 1/hr.

(iii) the filtration was performed with a 100 second (manually set)interval between backwashes. The average production rate was 946 1/hr.

Various modifications may be made in details of design, construction andmode of operation without departing from the scope and ambit of theinvention. For example, the methods and apparatus of the invention maytake account of other factors such as the cost of the cleaning gas andwear and tear on the filter unit. Thus, the optimum time for backwashingto achieve maximum average flux may be extended to take account of suchfactors.

We claim:
 1. A method of operating a microporous hollow fibre filtercomprising the steps of:(i) applying a liquid feedstock to be filteredto the outer surface of the filters whereby:(a) some of the liquidpasses through the walls of the fibres to be drawn off as clarifiedliquid or filtrate from the fibre lumens, (b) at least some of thesolids are retained on or in the fibres with the non-retained solidsbeing removed from the filter with the remainder of the liquid (ii)discharging the retained solids by applying a pressurised liquid and/orgas backwash, (iii) calculating from the rate of diminution of flow offiltrate after each application of pressurised liquid and/or gaseousbackwash an equation expressing the relationship between filtrate flowand time, and, (iv) allowing for the time lost in each backwash cycleand the amount of filtrate lost in each backwash cycle, (v) calculatingfrom the filtrate loss, the time loss and the the relationship betweenfiltrate flow and time, the optimum time and pattern of application ofsequential liquid or gaseous backwashes, and, (vi) effecting thebackwash at the optimum time.
 2. A method according to claim 1 andincluding the steps of implementing a chemical cleaning of the fibresafter a series of backwashes and calculating from the rate of decreaseof peak value of filtrate flow after each backwash cycle and the amountof time and filtrate lost in chemical cleaning, the optimum time forshut down for chemical cleaning.
 3. Apparatus for filtering a feedstockand for carrying out a predetermined frequency of liquid and/or gaseousbackwashes of the filtering apparatus comprising:(i) means for applyinga feedstock to be filtered to the outside surface of porous hollowfibres contained in a shell or housing, and for withdrawing clarifiedliquid or filtrate from the lumens of the fibres, (ii) means forapplying through the fibre lumens liquid and/or gaseous backwashes thatpass through the walls of the fibres, (iii) means for measuring the rateof decrease in filtrate flow rate, (iv) means for calculating theoptimal backwash frequency taking account of the rate of decrease infiltrate flow rate, loss of filtrate and time involved in a backwashcycle, and, (v) means for applying the calculated optimal backwashfrequency to the fibres in the filter.
 4. Apparatus for automaticallyapplying a predetermined pattern of sequential liquid and gaseousbackwashes whilst maintaining a dynamic membrane layer on the surface ofthe filter fibres, as described above said apparatus comprising:(i)means for applying a feedstock to be filtered to the outside surface ofporous hollow fibres contained in a shell or housing and for withdrawingfiltrate from the lumens of the fibres, (ii) means for applying throughthe fibre lumens liquid and gaseous backwashes that pass through thewalls of the fibres, (iii) means for automatically applying thepredetermined backwash pattern to the fibres in the filter, (iv) meansfor detecting the quality of the filtrate and redirecting it back to thefeedstock if the quality is unacceptable, (v) means for measuring therate of decrease in filtrate flow rate, or flux, (vi) means forcalculating the optimal backwash frequency taking account of the loss offiltrate and time involved in a backwash cycle, and, (vii) means forapplying the calculated optimal backwash frequency to the fibres in thefilter.
 5. Apparatus for filtering a feedstock and for carrying outliquid and/or gaseous backwash cycles, said apparatus comprising:(i)means for applying a feedstock to be filtered to the outside surface ofporous hollow fibres contained in a shell or housing, and forwithdrawing clarified liquid or filtrate from the lumens of the fibres,(ii) means for applying through the fibre lumens liquid and/or gaseousbackwashes that pass through the walls of the fibres, (iii) means fordetermining the instantaneous filtrate flow rate at any point in time,(iv) means for measuring the integrated filtrate flux over time sincethe last backwash or chemical cleaning cycle, (v) means for applying abackwash cycle to the fibres when the integrated filtrate flux equalsthe instantaneous filtrate flux multiplied by the sum of the period oftime elapsed since the last backwash plus the time taken for thebackwash cycle.